Diverse near neighbor problem

Authors:
Sofiane Abbar;Sihem Amer-Yahia;Piotr Indyk;Sepideh Mahabadi;Kasturi R. Varadarajan
Affiliations:
QCRI, Doha, Qatar;CNRS, LIG, Paris, France;MIT, Cambridge, MA, USA;MIT, Cambridge, MA, USA;U Iowa, Iowa City, IA, USA
Venue:
Proceedings of the twenty-ninth annual symposium on Computational geometry
Year:
2013

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Abstract

Motivated by the recent research on diversity-aware search, we investigate the k-diverse near neighbor reporting problem. The problem is defined as follows: given a query point q, report the maximum diversity set S of k points in the ball of radius r around q. The diversity of a set S is measured by the minimum distance between any pair of points in $S$ (the higher, the better). We present two approximation algorithms for the case where the points live in a d-dimensional Hamming space. Our algorithms guarantee query times that are sub-linear in n and only polynomial in the diversity parameter k, as well as the dimension d. For low values of k, our algorithms achieve sub-linear query times even if the number of points within distance r from a query $q$ is linear in $n$. To the best of our knowledge, these are the first known algorithms of this type that offer provable guarantees.